Precise vector nanoelectromechanical

Abstract

A method for operating a scanning probe microscope is provided. The method includes the following steps: (i) positioning a first measurement point on the surface of the cantilever at a first position offset from the zero point; (ii) measuring the cantilever motion at the first position while the tip interacts with the sample; (iii) positioning a second measurement point on the surface of the cantilever at a second position offset from the zero point and the first position; (iv) measuring the cantilever motion at the second position while the tip interacts with the sample; and (v) calculating one or more components of the cantilever motion based on the relative position of each of the first and second positions with respect to the zero point and the measurements taken from the first and second positions in steps (ii) and (iv).

Description

Invention Field

[0001] This invention relates to the operation of scanning probe microscopes (SPMs), such as atomic force microscopes (AFM).

[0002] References

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[0075] Stowe, TD., Yasumura, K., Kenny, T.W., Botkin, D., Wago, K., Rugar, D. *Applied Physics Letters*, 1997, 71, 288. doi: 10.1063 / 1.119522 Background of the Invention

[0077] Atomic force microscopy (AFM) has become a mainstay of nanoscience and technology due to its high resolution, environmental versatility, and the combination of countless measurement modes. Typically, AFM is based on a flexible microfabricated cantilever 1000, which has a sharp tip at its end 1020 or 1030 that interacts with the sample 1500. Details of AFM are well known in the art and described elsewhere, including in U.S. Patent 9,841,436.

[0078] Most AFM measurements measure only one strain component of the 3D tip motion vector. This component is typically the vertical deflection component δz of the cantilever away from its equilibrium position. Then, Hooke's law is applied. The force can be estimated from the observable deflection, where It is the spring constant of the cantilever at the tip position, and It is the displacement of the tip.

[0079] The first AFM used a tunneling detector. Shortly thereafter, various optical interferometric detection methods were demonstrated. In 1986, Martin and Wickramasinghe demonstrated an AFM using a sensitive heterodyne laser interferometer. They reported a high-frequency noise baseline of approximately 10. This performance is cited at “alternating” frequencies, which may be well above 10 kHz, although there are no citation restrictions in the paper. This heterodyne interferometer is sensitive to fluctuations in optical path length and is therefore unsuitable for low-noise, low-frequency measurements. To some extent, this is also the case with more modern heterodyne detectors, such as the laser Doppler vibrometer used in the commercial Cypher IDS system from Oxford Instruments. Many other interferometric detection schemes have been used in AFM, including the Michelson interferometer reported by Erlandsson et al. in 1987. In 1988, Rugar et al. made a significant improvement, in which stability to low-frequency fluctuations was improved by using a fiber-coupled interferometer with a very small optical cavity. While Rugar has excellent noise performance (numbers needed here) because it is a single-phase interferometer, the dynamic measurement range is only a fraction of the wavelength of light. More recently, the Fabry-Perot interferometer has further developed this concept, where the fineness of the optical cavity increases the noise floor to approximately 1. While this is an impressive noise floor, it comes at the cost of an extremely limited dynamic range. Although Hoogenboom et al. did not explicitly mention the dynamic range, they reported a maximum amplitude of 1 nm in their paper. A year after Rugar's fiber interferometer was introduced, Shonenberger and Alvarado reported an orthogonal phase differential interferometer. Because this is a differential measurement, with the two measurement locations being the base and vibrating end of the cantilever, the common-mode low-frequency noise is significantly reduced, enabling a remarkable ~10⁻¹⁰ resolution. Noise floor. Compared to single-phase locking, detection of quadrature components also means that it does not have to operate within a limited cavity size range, and the dynamic range of the cantilever is a few micrometers or larger. Although this differential method has been used by some other groups, it has not been widely adopted, possibly due to the complexity of optical design, the stability of beam-splitting optics, and more importantly, because beam detectors (OBD), introduced in 1990, are relatively easy to build and implement.

[0080] OBD solutions offer a relatively inexpensive, low-noise detection method that is virtually ubiquitous in the AFM field, with most commercial AFM systems based on it. The OBD method is the most commonly used technique in cantilever deflection measurement. In this method, a laser emitted from a solid-state diode is directed to the back of the cantilever and then detected by a position-sensitive detector (PSD), which consists of two closely spaced photodiodes. The output signals of these photodiodes are collected by a differential amplifier.

[0081] When the cantilever undergoes angular displacement, one photodiode collects more light than the other, generating an output signal. This output signal (obtained by calculating the difference between the photodiode signals and normalizing their sum) is proportional to the cantilever's deflection. This means the OBD detector measures the slope. Instead of measuring the displacement of the position. This is in Figure 1 As shown in 1800, where the cantilever 1000 is at point measurement position 1010 The location has a position-dependent displacement of 1050 and a related deflection. .

[0082] The development of OBD allows for the independent measurement of torsional bending of cantilever beams while they are deflecting in the normal direction. This allows for the use of techniques such as transverse force microscopy (LFM). LFM measurements allow for the measurement of frictional forces in a wide variety of materials. LFM measurements are considered to be affected by high uncertainties associated with the difficulty in calibrating both transverse measurement sensitivity and transverse stiffness. In AFM, the cantilever is generally relatively compliant along the z-axis, but less compliant along other axes.

[0083] Invented in 1987, LFM, also known as friction force microscopy (FFM), has gained increasing application in recent years. It is used to map the surface properties of various materials, such as polymers, thin films, and photolithographically patterned surfaces. LFM distinguishes chemical groups by measuring the forces interacting with chemically functionalized tips, making it a form of chemical force microscopy (CFM). It is typically performed by measuring force-distance curves (FDC) and is closely related to the adhesive force value. One problem with OBD detection methods is the misalignment of the quadrant detector and the reflected beam axis. To accurately attribute the measured signals to their respective driving forces, crosstalk-free detection of the vertical and lateral signals is crucial. Typically, for OBD microscopy, these two signals are not completely separated due to misalignment between the plane of the laser beam used for readout and the direction of the position-sensitive detector. (Munz, J., PhD in Physics: Applied Physics 43 (2010) 063001) Figure 3 The image shows a good example of this misalignment.

[0084] To address this issue, adjustments can be made using a device involving shear piezoelectricity while the tip is in contact with the sample. Correction for this crosstalk has been discussed in "Crosstalk Compensation in Optical Lever Deflection Methods Used in Atomic Force Microscopy" and in Hoffmann Á, Jungk T, and Soergel E, *Review of Scientific Instruments*, 2007, 78 016101. These methods are somewhat cumbersome and, despite the importance of clearly separating these signals, have not yet been widely adopted. Researchers analyzed optical crosstalk by observing the variation of the friction ring with sample height and found that the misalignment factor can vary significantly with the reflection point on the cantilever. In tip-scanning AFM, which means that the cantilever, rather than the sample, is moved to create relative motion between the tip and the sample, crosstalk can occur even with an undeformed cantilever if the tip-scanning system axis is not properly aligned with the optical detector axis.

[0085] Real-time correction of the PSD signal is a challenge for most commercial AFM systems, but data processing schemes and analysis methods have been proposed to quantify and adjust crosstalk. One approach involves an affine transformation applied to the measured voltage. Another approach models the entire detection system, allowing for parametric simulations to study the effects of misalignment in the beam path and to more effectively quantify the crosstalk coefficient. These methods typically require laborious testing or involve signal processing, which can introduce noise and other undesirable characteristics into the signal. Furthermore, this correction process often needs to be repeated each time a new cantilever is used, even if the spot position changes on the same cantilever back side (see, for example, Asay DB and Kim SH, 2006, Review of Scientific Instruments 77 043903).

[0086] While some degree of mechanical crosstalk is likely present in most cantilever setups, its measurement and quantification are often overlooked. Finally, it should be noted that the same argument applies to vertical measurements. Crosstalk from lateral motion in the vertical OBD signal can lead to uncontrollable errors in vertical measurements. By mitigating crosstalk, it is possible to reduce the variability in data obtained from different experimental setups, where measurement data become less dependent on instrument-specific characteristics, cantilever selection, and other experimental variations, resulting in more consistent and reliable results across different laboratories.

[0087] There are many more detailed descriptions and discussions of the LFM / friction calibration method in the literature. For example, J. Phys. D 43063001 (2010).

[0088] Another important factor that almost all AFM (Automatic Modeling) systems must consider is that the cantilever's reference frame rarely matches that of the sample. Generally, for practical design reasons, the cantilever is usually slightly tilted relative to the sample surface (see...). Figure 1 The sample roughness and surface structure increase complexity, which means that the tip-sample force is rarely (if any) parallel to the z-axis of the cantilever. Figure 1 A representation of a prior art cantilever 1000 is shown. For optical detection AFM, light is focused onto point 1010 at the top of the cantilever, and the reflected light is then used to estimate the motion of the tip. The tip is typically located below the top surface 1020, or in some cases, visible from the top 1021. Generally, the cantilever body forms a small angle θ with the sample surface.

[0089] In other words, in some cases, it is useful to consider the cantilever parallel to the sample because this can greatly simplify the analysis.

[0090] In the following sections, we use piezoelectric force microscopy (PFM) as a representative technique for demonstrating the capabilities of analog force microscopy (AFM). PFM is one of the most widely used techniques for studying piezoelectric and ferroelectric properties. It offers high spatial resolution and sensitivity. In PFM, the local electromechanical response is measured by applying a modulated potential to the tip of the cantilever and then measuring the mechanical response at the same frequency. The simple idea is that cantilever vibration is caused by the inverse piezoelectric effect.

[0091] Since its inception in 1996, this technique has been used to study wide arrays of nanoscale piezoelectric and ferroelectric materials, in addition to other materials with electromechanical coupling. Inevitably, some surprises have occurred in this process, most notably the use of PFM to treat materials that shouldn't be piezoelectric, yielding many "strange" seemingly piezoelectric results. Meanwhile, there is a trend towards studying systems with thinner and smaller features and materials with weaker inverse piezoelectricity. These weaker piezoelectrics are more susceptible to background effects, such as long-range electrostatics and other types of crosstalk effects, including morphological and electrical effects.

[0092] A characteristic of piezoelectric responses in materials is their three-dimensional response to an applied electric field. This response, in turn, leads to three-dimensional translation of the tip. Rodriguez and Kalinin et al. pointed out that the sensitivity to longitudinal tip displacement can be comparable to, or even more sensitive to, normal displacement. They also hypothesized that the significant difference between normal and longitudinal measurements could be explained by the insertion of a friction-slip probe. By rotating the sample beneath the cantilever probe, an angle-resolved PFM (AR-PFM) technique is used to observe in-plane ferroelectric elements. AR-PFM can provide both a vector diagram of the sample response and serve as a detector of the presence of measurable longitudinal forces. A significant drawback is that it requires aligning the tip and sample at each new angle and necessitates practical image drift and distortion correction. While the results of this method are promising, it is both cumbersome and error-prone due to the large number of images required.

[0093] The force acting on the tip is typically a three-dimensional vector, with coordinates designated as x, y, and z in the cantilever's reference frame. The cantilever's response to the force acting on the tip depends on a variety of factors, including the excitation frequency, details of the cantilever's shape and dimensions, and other factors known in the art.

[0094] It is convenient to establish a reference frame (x', y', and z') for the sample. These two reference frames are tilted at an angle θ relative to each other. In most applications, force measurements are taken in the z-direction (in the cantilever's reference frame). This axis of the cantilever is typically a "soft" axis, meaning it is the axis with minimum stiffness or spring constant. The sensor travels in different directions ( , and The stiffness of these vertices typically varies considerably. Since the forces at the tip apex are usually 3D, the vertex will respond to the forces exerted by the vertices. The given force causes the object to move, where i = x, y, or z.

[0095] To date, most OBD PFM measurements assume that motion is restricted to a component perpendicular to the sample surface. This has proven sufficient for a wide range of applications, where the cantilever's "z" motion has been used to measure force and displacement to create feedback images using low-frequency, sub-resonance, and resonance, as well as multi-frequency techniques.

[0096] In 2015 (Labuda and Proksch), we demonstrated that interferometric detection allows for the direct probing of motion at the tip of an AFM cantilever. In particular, they were able to demonstrate that the effects of electrostatic interactions between the cantilever body and the charged sample surface can be isolated from the local strain beneath the tip, thus providing a better quantification of the inverse piezoelectric coefficient. This method has been successfully used to better identify the origins of electromechanical responses in a variety of emerging materials.

[0097] In summary, an ideal calibration method should provide high accuracy, traceability to SI units, and the ability to quantify and eliminate crosstalk. To ensure widespread adoption, it should also be compatible with commercial deployments, user-friendly, and applicable to various cantilever shapes and lateral force magnitudes. While various methods for calibrating lateral forces have been demonstrated, further research is needed to achieve the required levels of accuracy, ensure consistency with general metrology standards, establish acceptance within the microscopy community and relevant user groups, and cover the entire range of forces from piconewtons to micronewtons. Summary of the Invention

[0098] As discussed above, the cantilever in an AFM is an extended, dynamic mechanical object. It responds to forces by moving in a manner determined by the frequency and location of the driving force, as well as the structural and material properties of the cantilever itself. For example, the cantilever will deflect in a relatively simple manner to a force applied to its tip and perpendicular to its long axis.

[0099] The tip of the AFM probe can move in three-dimensional space. It is typically assumed that the AFM OBD detector only measures the vertical deflection component of the cantilever as it moves away from its equilibrium position. However, the longitudinal component This will also affect the signal. In other cases, among other factors, the lateral component will also be affected due to misalignment between the OBD detector axis and the cantilever. It may also affect the OBD signal in an uncontrolled manner.

[0100] This measurement of motion is how atomic force microscopy determines the forces acting between the cantilever tip and the sample under study. Because these forces are three-dimensional and can vary considerably in frequency and magnitude, a good understanding of cantilever dynamics and motion is essential to correctly interpret the forces acting on the sample tip. Furthermore, nonlocal forces exist between the sample and the cantilever body. These may include long-range electrical forces or viscous damping forces from the atmosphere surrounding the cantilever.

[0101] This invention describes a method for determining the tip trajectory of a mechanical probe in multiple dimensions (preferably three dimensions). For example, prior art measurement teachings place the detection point directly above the probe tip to measure the vertical motion of the tip; in this case, we show that by placing it in other locations, highly accurate measurements of the vertical and other motion components can be achieved.

[0102] Various aspects of the invention

[0103] A first aspect of the present invention provides a method of operating a scanning probe microscope. The scanning probe microscope includes: a probe having a cantilever with a tip, wherein the cantilever includes a zero point on a surface of the cantilever; a sample and a sample holder arranged to hold the sample for measurement using the tip of the cantilever; a light source arranged to emit one or more beams of light onto the surface of the cantilever, each beam of light forming a measurement point on the surface of the cantilever; an optical assembly configured to adjust the position of each measurement point on the surface of the cantilever; and a photodetector assembly for measuring light reflected from the surface of the cantilever to measure the movement of the cantilever based on the light reflected from each measurement point. The method includes the following steps: (i) positioning a first measurement point on the surface of the cantilever at a first position offset from the zero point; (ii) measuring the cantilever motion at the first position while the tip interacts with the sample; (iii) positioning a second measurement point on the surface of the cantilever at a second position offset from both the zero point and the first position; (iv) measuring the cantilever motion at the second position while the tip interacts with the sample; and (v) calculating one or more components of the cantilever motion based on the relative position of each of the first and second positions with respect to the zero point and the measurements taken from the first and second positions in steps (ii) and (iv).

[0104] Typically, when the tip interacts with the sample, forces act on the tip from all directions, affecting the resulting cantilever motion. This method advantageously allows the components of the cantilever motion to be calculated individually. These components are typically vector components of the forces acting in different directions. This beneficially provides additional information related to cantilever dynamics when the tip interacts with the sample.

[0105] The zero point is the position on the cantilever where the cantilever motion is affected only by the vertical force. The first and second positions are on the surface of the cantilever and are offset from the zero point on the cantilever surface. There may be more than one zero point on the cantilever; in this case, both the first and second positions are offset from each zero point. At the first and second positions, the cantilever motion is affected by the vertical force, and also by lateral and longitudinal forces, i.e., forces perpendicular to the vertical force in the sample plane. Therefore, each measurement step (ii) and (iv) of the method returns a combination of components. The first and second positions are also offset from each other, which advantageously provides two different measurements of the cantilever motion, which can be combined in step (v) to calculate one or more components of the cantilever motion.

[0106] The interaction between the tip and the sample typically involves moving the tip toward the sample to increase the interaction force. Preferably, the scanning probe microscope also includes an actuator assembly configured to move the cantilever relative to the sample holder. Typically, this actuator assembly is configured to adjust the distance between the tip and the sample along the optical axis of the light source or along an axis substantially parallel to that axis to account for cantilever tilt. The actuator assembly also moves the tip and the sample relative to each other in a direction perpendicular to the first axis to measure different points on the sample surface. This same actuator assembly may optionally vary the relative positions of the cantilever and the light source and / or optical and / or photodetector assemblies.

[0107] The terms "each" beam and "each" measurement point mentioned above should not be interpreted as meaning that multiple such beams and points must exist. Rather, these are references to a single beam among the one or more beams mentioned above and to each measurement point among the one or more measurement points mentioned above (respectively). Thus, when the light source is configured to emit (only) a single beam onto the surface of the cantilever, that beam forms a (single) measurement point on the surface of the cantilever; and the position of that measurement point can be adjusted; and a photodetector assembly is used to measure the light reflected from that measurement point to measure the cantilever motion. However, as described below, in some embodiments, the use of multiple beams and corresponding measurement points is preferred.

[0108] The light source preferably has a single optical axis facing the cantilever. Preferably, the optical axes of one or more beams emitted by the light source will be substantially parallel to the optical axis of the light source (and therefore substantially parallel to each other in the case of multiple beams).

[0109] Optionally, the scanning probe microscope also includes an actuator assembly configured to adjust the distance between the tip and the sample along the optical axis of the light source. Therefore, this actuator assembly can be used to adjust the interaction between the tip and the sample. The scanning probe microscope can be used in different scanning modes, such as "tapping mode" and "contact mode".

[0110] In tapping mode, the actuator assembly can be configured to drive the cantilever at a driving frequency, thereby adjusting the distance between the tip and the sample. The cantilever motion is typically influenced by the interaction between the tip and the sample while adjusting the distance between them.

[0111] Alternatively, in contact mode, the actuator assembly can be configured to engage the tip toward the sample and disengage the tip away from the sample. The actuator assembly can be used to alter the interaction between the tip and the sample by lowering or raising the tip relative to the sample to increase or decrease the interaction force, respectively. Cantilever motion is typically influenced by the interaction between the tip and the sample while altering the interaction force. Optionally, in contact mode, the distance between the tip and the sample may become negative as the interaction force increases. Negative disengagement means that a portion of the tip lies below the upper surface of the original, undisturbed surface.

[0112] Preferably, each of the one or more components calculated in step (v) is parallel to or perpendicular to the optical axis of the light source.

[0113] This means that each of the one or more components calculated in step (v) is parallel to or perpendicular to the optical axis of the light source. In the example where two or more components are calculated in step (v), the two or more components may optionally include at least one parallel component and at least one perpendicular component.

[0114] Advantageously, this can be used to calculate the pure cantilever displacement (i.e., the vertical motion of the cantilever) as well as the cantilever motion components perpendicular to the vertical motion. The vertical components of the cantilever motion can be referred to as the lateral and longitudinal components of the cantilever motion, which are typically in the plane of the sample.

[0115] Preferably, at least one of the components calculated in step (v) is perpendicular to the optical axis of the light source and aligned with the major axis or minor axis of the cantilever, wherein the minor axis is perpendicular to the major axis along the surface of the cantilever.

[0116] Typically, the cantilever can be substantially planar, having a major axis and a minor axis in a plane including the cantilever surface. The cantilever preferably has a supported end and a free end. The supported end is typically supported by a probe, and the tip is typically positioned at the free end, away from the supported end. Preferably, the major axis is an axial direction extending between the free end and the supported end of the cantilever, which may be perpendicular to the edge of the probe. Most preferably, the cantilever is symmetrical about the major axis. Also preferably, there is a zero point located on the major axis. Preferably, the minor axis is orthogonal to the major axis in a plane of the cantilever surface. Most preferably, there is a zero point located substantially where the major and minor axes intersect each other. Most preferably, the major and minor axes intersect each other and are substantially in a straight line with the tip. Optionally, for slender cantilevers, the major axis is preferably parallel to the elongation direction. The major and minor axes of the cantilever referred to herein refer to these directions.

[0117] Advantageously, when one component of the cantilever motion is aligned with the major or minor axis of the cantilever, the lateral (i.e., torsional) and longitudinal (i.e., bending) components of the cantilever motion can be directly detected. This also advantageously simplifies the calculations in step (v).

[0118] Preferably, step (v) may include: calculating a first component of the cantilever motion based on the relative position of each of the first and second positions relative to the zero point and measurements taken from the first and second positions in steps (ii) and (iv); and calculating a second component of the cantilever motion based on the relative position of each of the first and second positions relative to the zero point and measurements taken from the first and second positions in steps (ii) and (iv); wherein the second component is perpendicular to the first component.

[0119] Optionally, the first component is parallel to the optical axis of the light source, and the second component is perpendicular to the optical axis of the light source. Typically, the second component is parallel to a straight line extending between the first and second positions.

[0120] Advantageously, this provides information about the two vertical components of the cantilever motion, allowing for further quantification of the cantilever dynamics.

[0121] Preferably, the first and second positions are symmetrical about the zero point. The symmetry of the first and second positions advantageously simplifies the steps of calculating one or more components. For example, the cantilever motion measured at the first and second positions may include corresponding components that are substantially equal in magnitude and opposite in sign: the cantilever motion measured at the first position may include a negative component in a first direction, while the cantilever motion measured at the second position may include a positive component in a first direction and substantially equal in magnitude.

[0122] Optionally, the first position may be offset from zero in a first direction, and the second position may be offset from zero in a second direction, wherein the second direction is substantially opposite to the first direction.

[0123] The components of the cantilever motion typically depend on the relative position of the measurement point with respect to the zero point. Preferably, the components of the cantilever motion depend on the offset direction of the measurement point and the zero point. Generally, when the first position deviates from the zero point in a first direction and the second position deviates from the zero point in a second direction, the components of the cantilever motion measured in step (ii) or (iv) each include a first component parallel to the optical axis of the light source and a second component perpendicular to the optical axis of the light source. In this case, the second component is typically parallel to the first direction, and therefore also parallel to the second direction.

[0124] Typically, in this case, the value of the first component parallel to the optical axis of the light source is the same for both the first and second positions, while the value of the second component perpendicular to the optical axis of the light source is different for both positions. In this way, the cantilever motion measured in steps (ii) and (iv) can be combined to determine the values ​​of the first and second components. Measurements taken at two different positions can advantageously be used to calculate the cantilever motion, typically using the two components that are perpendicular to the optical axis.

[0125] Optionally, the straight line drawn between the first and second positions can be substantially parallel to the major axis of the cantilever, or the straight line drawn between the first and second positions can also be substantially parallel to the minor axis of the cantilever. As mentioned above, the minor axis is perpendicular to the major axis along the surface of the cantilever.

[0126] Optionally, the first position can be located on the major axis and the second position can be located on the minor axis, or the first position can be located on the minor axis and the second position can be located on the major axis.

[0127] Preferably, the first and second positions can each be located on the long axis of the cantilever, or the first and second positions can each be located on the short axis of the cantilever.

[0128] When the first and second positions are respectively located on the major or minor axis of the cantilever, it is advantageous to use measurements from only two positions on the surface of the cantilever to determine the motion of the cantilever about the minor or major axis, respectively.

[0129] When the first and second positions are symmetrical about the zero point, the first component is generally substantially the same when the cantilever motion is measured at each of the first and second positions. However, if the positions are symmetrical about the zero point, the second component generally has substantially the same magnitude, but the sign is usually opposite when the cantilever motion is measured at each position.

[0130] Typically, cantilever motion can be cantilever displacement or cantilever deflection. Optionally, only cantilever displacement or only cantilever deflection can be measured. Alternatively, both cantilever displacement and cantilever deflection can be measured.

[0131] Advantageously, when measuring both cantilever displacement and cantilever deflection, more information about the cantilever motion can be obtained for each measurement point. Furthermore, the additional measurements obtained through over-constraint fitting can be used to validate and cross-check the values ​​of one or more components calculated in step (v).

[0132] Preferably, when the cantilever motion is cantilever displacement, an interferometric displacement sensor is used to measure the cantilever motion. Preferably, when the cantilever motion is cantilever deflection, a beam deflection sensor is used to measure the cantilever motion.

[0133] Typically, when the tip interacts with the sample, the cantilever undergoes both displacement and deflection. The amount of displacement and deflection depends on the tip-sample interaction.

[0134] Cantilever displacement, measured by monitoring changes in the cantilever's position relative to a surface, provides information about the separation between the tip and the sample. Interferometric displacement sensors typically achieve this by measuring changes in the distance between the cantilever surface and a reference point. Cantilever displacement is usually a distance.

[0135] Cantilever deflection provides information about the cantilever's bending. Using beam deflection, the bending of the cantilever causes the beam to deflect by a corresponding amount, thus providing information about the deflection angle.

[0136] Optionally, the interferometric displacement sensor may include a differential interferometer. The differential interferometer advantageously provides two beams whose optical path lengths can be compared. Typically, the first beam can be used to form a reference point, while the second beam can be used to form a measurement point on the surface of the cantilever. The measurement point can be used as one of the measurement points described above (or as more than one measurement point in serial acquisition mode). The reference point can be formed on the surface of the probe supporting the cantilever.

[0137] Alternatively, the first beam of the differential interferometer can be used to form a first measurement point on the surface of the cantilever, and the second beam of the differential interferometer can be used to form a second measurement point on the surface of the cantilever. Advantageously, this provides two measurement points that are a known distance apart. In the parallel acquisition method described above, the first and second measurement points can be used simultaneously as two measurement points. Therefore, this simplifies the location of the measurement points, since steps (i) and (iii) can be performed simultaneously using a single interferometer.

[0138] Optionally, step (ii) may include: (a) measuring the cantilever displacement at a first position while the tip interacts with the sample; and (b) measuring the cantilever deflection at the first position while the tip interacts with the sample; and / or step (iv) may include: (a) measuring the cantilever displacement at a second position while the tip interacts with the sample; and (b) measuring the cantilever deflection at the second position while the tip interacts with the sample.

[0139] Advantageously, measuring cantilever displacement and cantilever deflection provides more information about the cantilever motion. This can be used to obtain more components and / or over-constraint data of the cantilever motion in order to verify the component values ​​calculated in step (v). For example, measuring displacement and deflection in step (ii) or step (iv) can be used to calculate three mutually perpendicular components of the cantilever motion. Measuring displacement and deflection in steps (ii) and (iv) can advantageously be used to provide further measurements, thereby addressing over-constraint fitting when calculating one or more components.

[0140] Over-constraint fitting may include calculating a first component of the cantilever motion using a first combination of measurements to obtain a calculated first component of the cantilever motion; and calculating the first component of the cantilever motion using a second combination of measurements to obtain a calculated second component of the cantilever motion. Verifying the calculated components may include comparing the calculated first component with the calculated second component. Theoretically, the calculated first and second components are expected to be identical, and therefore any difference between the calculated first and second components can advantageously indicate experimental variations. For example, a tip typically degenerates over time, which may cause differences between the calculated first and second components.

[0141] Alternatively, steps (i) through (v) can be performed sequentially, i.e., sequentially. This can be referred to as serial acquisition, where the steps of the method are typically performed sequentially, i.e., step (i), step (ii), step (iii), step (iv), and then step (v). This advantageously means that the setup of the scanning probe microscope can be simplified.

[0142] Alternatively, steps (ii) and (iv) can be performed simultaneously. That is, the method may include simultaneously measuring the cantilever motion at the first and second positions while the tip interacts with the sample. This may be referred to as parallel acquisition, in which the cantilever motion at the first and second positions is measured simultaneously. This is preferably achieved using a light source arranged to emit two beams onto the surface of the cantilever. Alternatively, this can be achieved using a single light-emitting device arranged to emit two beams, or using two light-emitting devices, each arranged to emit one beam. The one or more light-emitting devices form part of the light source.

[0143] Advantageously, parallel acquisition is faster than serial acquisition. Parallel acquisition also avoids any errors that might otherwise be introduced by the movement of measurement points between serial acquisition steps. Furthermore, by simultaneously measuring the cantilever motion at the first and second positions, tip-based effects, such as tip degradation due to imaging, can be avoided.

[0144] When steps (ii) and (iv) are performed simultaneously, steps (i) and (iii) are preferably performed before steps (ii) and (iv). Steps (i) and (iii) may be performed at different times or at the same time. Preferably, if the beams forming the first and second measurement points are linked, for example, if they are emitted from the same light emitting device, steps (i) and (iii) are preferably performed simultaneously. Alternatively, if the beams forming the first and second measurement points are controlled separately, steps (i) and (iii) may be performed at different times by adjusting the measurement points sequentially. Step (i) may be performed before or after step (iii). Step (v) is generally performed after steps (ii) and (iv).

[0145] Optionally, if step (ii) includes: (a) measuring the cantilever displacement at a first position while the tip interacts with the sample; and (b) measuring the cantilever deflection at the first position while the tip interacts with the sample; and / or if step (iv) includes: (a) measuring the cantilever displacement at a second position while the tip interacts with the sample; and (b) measuring the cantilever deflection at the second position while the tip interacts with the sample, steps (ii)(a) and (iv)(a) may be performed simultaneously with steps (ii)(b) and (iv)(b), or steps (ii)(a) and (iv)(a) may be performed before or after steps (ii)(b) and (iv)(b), at different times. Optionally, steps (ii)(a) and (ii)(b) may be performed using the same beam emitted by the light source. Similarly, steps (iv)(a) and (iv)(b) may be performed using the same beam emitted by the light source. This advantageously simplifies the SPM arrangement because a single beam can be used to measure both the displacement and deflection of the cantilever surface. Alternatively, steps (ii)(a) and (ii)(b) can be performed using separate beams. Similarly, steps (iv)(a) and (iv)(b) can be performed using separate beams. As stated above, separate beams can be used to obtain measurements simultaneously or sequentially.

[0146] Preferably, step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first and second positions with respect to the zero point, the height of the tip, and measurements taken from the first and second positions in steps (ii) and (iv).

[0147] The tip height is typically measured perpendicular to the surface of the cantilever and can be advantageously used to calculate the first and second lever arms separately by combining the relative positions of each of the first and second positions with respect to the zero point. Each lever arm (also referred to as the gain factor) is the ratio of the distance between the measurement point and the zero point position to the tip height.

[0148] Tip height can be measured in a variety of ways. For example, an optical microscope or an electron microscope can be used to measure tip height to obtain an image of the tip, and the tip height can be measured based on the obtained image.

[0149] Optionally, the method may further include the following steps: (vi) positioning a third measurement point on the surface of the cantilever at a third position offset from the zero point and the first and second positions; and (vii) measuring the cantilever motion at the third position while the tip interacts with the sample. Step (v) may include calculating one or more components of the cantilever motion based on the relative position of each of the first, second, and third positions relative to the zero point and the measurements taken from steps (ii), (iv), and (vii) at the first, second, and third positions.

[0150] Advantageously, this makes it possible to calculate additional components of the cantilever motion in step (v). For example, the three unknowns can be determined by measuring the cantilever motion at three different locations. As mentioned above, further constraints can be imposed by measuring the displacement and deflection at one or more locations.

[0151] Optionally, the method may further include the following steps: (viii) positioning a fourth measurement point on the surface of the cantilever at a fourth position, offset from the zero point and from the first, second, and third positions; and (ix) measuring the cantilever motion at the fourth position while the tip interacts with the sample. Step (v) may include calculating one or more components of the cantilever motion based on the relative position of each of the first, second, third, and fourth positions relative to the zero point and the measurements taken from steps (ii), (iv), (vii), and (ix) at the first, second, third, and fourth positions.

[0152] Advantageously, this provides additional measurements to over-constrain the fit and validate the components calculated as described above. The over-constraint of the data can be advantageously used to monitor the temporal correlation of the measurements. Temporal correlation, i.e., the change of the measured cantilever motion values ​​over time, can be recorded. Optionally, the temporal correlation of the measurements can be modeled to determine correction factors to be applied to subsequent measurements of the cantilever motion. This advantageously offsets the temporal correlation factor of the cantilever motion, thus allowing for more accurate comparisons between measurements.

[0153] For example, the cantilever motion measured in steps (ii) and (iv) can be used to calculate the component of the cantilever motion parallel to the optical axis of the light source, and the same component can be calculated using the cantilever motion measured in steps (vii) and (ix). The calculated values ​​can then be compared.

[0154] Optionally, the method may further include the steps of: (x) positioning the fifth measurement point at a zero point on the surface of the cantilever; and (xi) measuring the cantilever motion at the zero point while the tip interacts with the sample. Preferably, step (xi) includes measuring the cantilever displacement at the zero point while the tip interacts with the sample. Advantageously, this provides an additional measurement of the vertical component of the cantilever motion, which can be compared with the calculated value in step (v).

[0155] For serial acquisition, steps (vi) through (ix) are typically performed sequentially, i.e., steps (vi), (vii), (viii), and (ix). Optionally, steps (vi) through (ix) may be performed after step (iv), with step (v) performed last. Alternatively, step (v) may be performed after step (iv) or after step (ix). Preferably, when step (v) is performed after step (iv), step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first and second positions relative to the zero point and measurements from steps (ii) and (iv) at the first and second positions. Preferably, when step (v) is performed only after step (ix), step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first, second, third, and fourth positions relative to the zero point and measurements from steps (ii), (iv), (vii), and (ix) at the first, second, third, and fourth positions. Typically, when step (v) is performed after step (iv) and after step (ix), step (v) after step (ix) includes calculating one or more components of the cantilever motion based on the relative position of each of the first, second, third, and fourth positions relative to the zero point and the measurements taken from the first, second, third, and fourth positions in steps (vii) and (ix).

[0156] For parallel acquisition, steps (vii) and (ix) can be executed simultaneously or at different times. Steps (vii) and (ix) can be executed simultaneously with steps (ii) and (iv), or at different times before or after steps (ii) and (iv).

[0157] Optionally, one or more components of the cantilever motion in step (v) may include a first, second, and third component, wherein the first, second, and third components are perpendicular to each other.

[0158] This means that the first and second components can be perpendicular to each other, the second and third components can be perpendicular to each other, and the first and third components can be perpendicular to each other.

[0159] Preferably, the first component is parallel to the optical axis of the light source, and the second and third components are perpendicular to the optical axis of the light source. Preferably, the second and third components are aligned with the major and minor axes of the cantilever, respectively.

[0160] Optionally, the third and fourth positions are symmetrical about the zero point. As described above regarding the first and second positions, the symmetry of the third and fourth positions advantageously simplifies the calculation of one or more components in step (v).

[0161] Optionally, the third and fourth positions may each be located on the major axis of the cantilever, or the third and fourth positions may each be located on the minor axis of the cantilever, wherein the minor axis is perpendicular to the major axis along the surface of the cantilever.

[0162] When the third and fourth positions are respectively located on the major or minor axis of the cantilever, as described above with respect to the first and second positions, it is advantageous to use measurements from only two positions on the surface of the cantilever to determine the motion of the cantilever about the minor or major axis.

[0163] Typically, the first and second positions can each be located on the major axis, and the third and fourth positions can each be located on the minor axis, or the first and second positions can each be located on the minor axis, while the third and fourth positions can each be located on the major axis. This arrangement advantageously allows the three components of the cantilever motion to be easily determined, and the vertical component of the cantilever motion can be over-constrained, which advantageously allows for cross-checking of the calculated components.

[0164] Depending on the oscillation mode, the cantilever may include multiple zero points. Preferably, the cantilever includes a zero point that is substantially aligned with the tip along the optical axis of the light source.

[0165] The location of zero can be identified using a variety of methods. For example, zero can be identified based on at least one of the following: user input, calibration procedures, values ​​stored in memory, or image recognition of the cantilever surface.

[0166] User input may include the user typing in an identifier for the cantilever, such as an identification number. Optionally, the zero point can be retrieved from memory based on the identified cantilever. Optionally, the user can view the cantilever and select the approximate location of the zero point based on user experience. For example, the user can estimate the location of the zero point based on the shape of the cantilever. Optionally, the user can use other equipment to image the tip (which could be the same image used to measure the tip height) and estimate the zero point based on the position of the tip, since the zero point is preferably substantially aligned with the tip, as described above.

[0167] Alternatively, the location of the zero point can be identified using automatic identification of the tip, for example, using a camera assembly. In some examples, the location of the zero point can be estimated based on cantilever deflection and oscillation amplitude or other SPM observables.

[0168] Alternatively, a calibration procedure can be used to estimate the location of the zero point. For example, the calibration procedure may include monitoring cantilever motion (e.g., displacement or amplitude) while modifying the interaction between the tip and the sample (e.g., by changing the spacing between the tip and the sample or by moving the tip within the sample plane). Depending on the location of the measurement point, modifying the interaction between the tip and the sample typically affects the cantilever motion to varying degrees. In this way, the location of the zero point can be estimated based on the change in cantilever motion in response to the changing tip-sample interaction.

[0169] The method preferably includes storing the position of the zero point, calculating two or more positions to locate the measurement point, and storing the position of each calculated position relative to the zero point. Preferably, the method also includes storing the measured tip height. If an image of the tip is captured using the integrated camera assembly described above, the method may include measuring the tip height by viewing the acquired image and subsequently storing the measured tip height. Alternatively, if the tip height is measured using a separate device, the method may include storing a tip height value input by the user. Advantageously, the stored value described above can be used in subsequent calculation steps.

[0170] Optionally, the method may include executing a computer program to cause the scanning probe microscope to perform each step of the method, or at least some steps of the method.

[0171] This greatly facilitates the user's operation of the scanning probe microscope, as these steps can be performed automatically.

[0172] Optionally, the steps of the method can be performed in a hybrid manner, wherein a computer program can be executed to cause the scanning probe microscope to perform some steps of the method, and other steps of the method can be performed manually by the user or using firmware or hardwired methods. For example, the user can perform steps (i) and (iii), and the computer program can perform steps (ii), (iv), and (v) of the method. Alternatively, after the computer program has performed one or more steps of the method, the user can provide confirmation that the program can proceed to the next step of the method. This alternatively represents an additional level of control and flexibility for the user, while benefiting from the simplicity of automation using the computer program.

[0173] Optionally, step (v) may include employing a rigid probe approximation, in which the cantilever is assumed to behave like a rigid body. Alternatively, step (v) may include employing an analytical model such as an Euler-Bernoulli beam theory model or other finite element methods. Advantageously, more complex models can be used to calculate the components of the cantilever's motion more accurately.

[0174] A second aspect of the invention provides a scanning probe microscope. The scanning probe microscope includes: a probe having a cantilever with a tip, wherein the cantilever includes a zero point on a surface of the cantilever; a sample holder arranged to hold a sample for measurement using the tip of the cantilever; a light source arranged to emit one or more beams of light onto the surface of the cantilever, each beam forming a measurement point on the surface of the cantilever; an optical assembly configured to adjust the position of each measurement point on the surface of the cantilever; and a photodetector assembly for measuring light reflected from the surface of the cantilever to measure the movement of the cantilever based on the light reflected from each measurement point. The scanning probe microscope is configured to perform the method according to the first aspect.

[0175] The advantages of the second aspect correspond to those of the first aspect. The optional features described in the first aspect also apply to the second aspect.

[0176] Preferably, the scanning probe microscope further includes an actuator assembly configured to move the cantilever relative to the sample, the actuator assembly optionally being configured to adjust the spacing between the tip and the sample along the optical axis of the light source, the sample being held by a sample holder. Advantageously, this can be used to modify the tip-sample interaction.

[0177] Optionally, the scanning probe microscope may also include a differential interferometer configured to position first and second measurement points on the surface of the cantilever at first and second positions respectively off-zero.

[0178] Advantageously, this allows for simultaneous measurement of cantilever motion at different locations. This advantageously enables parallel acquisition using a simple setup within a scanning probe microscope.

[0179] A third aspect of the invention provides a probe for performing the method according to the first aspect. The probe has a cantilever with a tip. The cantilever includes an unsupported first end and a second end supported by the probe, wherein the tip is disposed at the first end. A first region of the cantilever has a wider width than a second region of the cantilever, wherein the first region is closer to the first end and the second region is closer to the second end. Optionally, the width of the cantilever may increase toward the first end along at least a portion of the cantilever length.

[0180] As stated in the first aspect, the width of the cantilever is measured parallel to the minor axis of the cantilever.

[0181] While not essential for the performance of the first aspect of the invention, it is advantageous that the probe according to the third aspect allows the measurement point to be located further away from the zero point. This increases the gain factor, which advantageously further improves the accuracy of the component calculated in step (v) of the first aspect.

[0182] This can be achieved in different ways depending on the shape of the cantilever. Optionally, the width of the first end can be greater than the width of the second end.

[0183] Typically, a cantilever may include a surface for receiving measurement points, the surface having a major axis and a minor axis. Preferably, the major axis and minor axis are as defined above in the context of the first aspect of the invention.

[0184] Optionally, the second end may include an elongated body having a substantially constant width along the long axis of the cantilever surface. The first end may include a region with a width greater than that of the elongated body.

[0185] In some examples, the region can be a polygonal region with four or five sides.

[0186] Optionally, the first region may have a substantially uniform width and / or the second region may have a substantially uniform width.

[0187] A fourth aspect of the present invention provides a method for operating a scanning probe microscope. The scanning probe microscope includes: a probe having a cantilever with a tip; a sample and a sample holder arranged to hold the sample for measurement using the tip of the cantilever; a light source arranged to emit one or more beams of light onto a surface of the cantilever, each beam forming a measurement point on the surface of the cantilever; an optical assembly configured to adjust the position of each measurement point on the surface of the cantilever; and a photodetector assembly for measuring light reflected from the cantilever surface to measure the motion of the cantilever based on the light reflected from each measurement point. The method includes the steps of: (a) positioning a first measurement point at a first location on the surface of the cantilever; (b) measuring a cantilever displacement at the first location while the tip interacts with the sample; (c) measuring a cantilever deflection at the first location while the tip interacts with the sample; and (d) calculating one or more components of the cantilever motion based on the cantilever displacement measured in step (b) and the cantilever deflection measured in step (c).

[0188] Advantageously, this method can be used to obtain measurements of cantilever motion from only one measurement point location. This allows for the calculation of one or more components of the cantilever motion without adjusting the measurement point location.

[0189] Preferably, the scanning probe microscope further includes an actuator assembly configured to move the cantilever relative to the sample, the actuator assembly optionally being configured to adjust the distance between the tip and the sample along the optical axis of the light source.

[0190] Preferably, an interferometric displacement sensor is used to measure the cantilever displacement, and a beam deflection method is used to measure the cantilever deflection.

[0191] Preferably, the cantilever includes a zero point on the surface of the cantilever, wherein the first position is the zero point.

[0192] Advantageously, when the first position is zero, the cantilever motion is only affected by the vertical force, so the measured cantilever displacement typically includes only the vertical component. The measured cantilever deflection typically includes at least two components, one of which is the vertical component. Therefore, when the first position is zero, the calculation of the non-vertical components of the cantilever motion is advantageously simpler.

[0193] A fifth aspect of the present invention provides a scanning probe microscope. The scanning probe microscope includes: a probe having a cantilever with a tip; a sample holder arranged to hold a sample for measurement using the tip of the cantilever; a light source arranged to emit one or more beams of light onto a surface of the cantilever, each beam forming a measurement point on the surface of the cantilever; an optical assembly configured to adjust the position of each measurement point on the surface of the cantilever; and a photodetector assembly for measuring light reflected from the surface of the cantilever to measure the movement of the cantilever based on the light reflected from each measurement point. The scanning probe microscope is configured to perform the method according to the fourth aspect.

[0194] Preferably, the scanning probe microscope further includes an actuator assembly configured to move the cantilever relative to the sample, the actuator assembly optionally being configured to adjust the spacing between the tip and the sample along the optical axis of the light source, the sample being held by a sample holder.

[0195] The advantages of the fifth aspect correspond to those of the fourth aspect. The optional features described in the fourth aspect also apply to the fifth aspect. Attached Figure Description

[0196] Figure 1 A prior art schematic diagram of the probe top side where the cantilever, detection point, tip, and sample are located.

[0197] Figure 2 Let be the zero point of the cantilever and the straight line.

[0198] Figure 3 For interferometer measurements.

[0199] Figure 4 To correct crosstalk in the rotating reference frame.

[0200] Figure 5 Fitting of over-constrained measurements.

[0201] Figure 6 This is an experimental example.

[0202] Figure 7 This is a combination of IDS and OBD.

[0203] Figure 8A top view of the interferometric solution. Detailed Implementation

[0204] A force applied to the tip in any of the three Cartesian directions can be obtained by using a cantilever with a known spring constant in a certain direction i. Hooke's Law The deflection is used to estimate, where i is x, y, or z. As an example, in the case of PFM, the tip motion can be estimated using a three-dimensional vector. (Bold characters represent vectors) to describe:

[0205]

[0206] Here, , and It is a Cartesian unit vector. In this expression, the motion of the tip is divided into slowly changing and rapidly changing parts. For the purposes of discussion, the slowly changing motion vector... This represents motion within the microscope feedback bandwidth and includes measurements of image force curves, cantilever preload and scanning motion, as well as other interactions with timescales smaller than the cantilever feedback loop response time. More rapidly changing portions... Modulations can originate from higher frequencies and typically include electromechanical responses modulated by voltage between the tip and the sample, high-frequency mechanical modulations that can test rheological responses, high-speed force mapping, contact resonance, heterodyne measurements, and many other high-frequency measurements known in the art.

[0207] The single (high-frequency) electromechanical measurement of cantilever motion can be similarly represented by a sine term. To describe, the sine term includes the measured amplitude. and phase The subscript "m" indicates a measurement of the cantilever motion. In these and related measurements, the amplitude vector is related to the local electromechanical strain of the moving tip.

[0208] The phase of tip motion is related to the polarization direction. Phase shifts can also be generated by other tip-sample interactions, including dissipative and viscoelastic interactions. Low-frequency components are important in other measurements such as tribology or rheology and need to be included in the analysis of experimental data.

[0209] Interferometry provides a method for measuring locations. Quantitative measurement of cantilever displacement. The interferometer measures displacement only along its axis. In the following sections, we use the interferometer's measurement position dependence to quantify the three-dimensional tip motion. We assume the interferometer axis is aligned with the cantilever's z-axis. This is the optical arrangement of the Cypher IDS used in this work.

[0210] The interferometer spot can be located at different positions on the back of the cantilever. In the following text, we define the origin of the coordinate system as the position directly above the tip vertex. Generally, the z-displacement of the cantilever in response to the vertex motion is influenced by all three dimensions of the tip motion. , and The effect of this. For small strains, this can be described by a simple Taylor expansion, given by:

[0211]

[0212] Equation (1) describes how the tip strain component is mixed into the position-dependent interferometer signal. The first two terms in Equation (1) represent the effect of motion parallel to the cantilever plane on the cantilever bending, while the third term is the vertical motion.

[0213] These components are defined as ,in or .

[0214] Figure 2 The diagram illustrates so-called zero points or lines in cantilever motion, determined by the geometric symmetry of the cantilever and the nature of the excitation acting on its tip. For example, if the tip shifts 2105 along the Y-axis, the cantilever will twist along that line. This means the displacement along the central longitudinal axis 2100 is zero. If the interferometer measurement point is along the central longitudinal axis X-axis, the measured displacement will be zero or approximately zero. On the other hand, the angular change at that position is not zero. This means that OBD measurements along the central axis will be sensitive to the torsion or bending of the cantilever. For the interferometer, if the measurement point is moved laterally away from the central longitudinal axis along the Y-axis, the displacement will now be non-zero (e.g., 2110 or 2120), where the interferometer will measure torsional motion. Therefore, the sensitivity of the tip to motion along the Y-axis can be varied by positioning the interferometer at different points along the transverse Y-axis. In another example, if the tip applies a large force to the sample, and the tip-sample position is adjusted along the X-axis or the X principal axis, the tip will experience a force along the X-axis. If the applied force is high enough, there will be another axis of symmetry 2200, where the displacement at the top of the cantilever will be essentially zero, and if the interferometer spot is placed along this axis of symmetry 2200, the response will be zero. A final example is shown in Figures 2260 and 2250, where the cantilever oscillates at the dwell frequency in these resonant frequency oscillations, where the antinode displacement is known to be minimum at 0. In this case, if there are nodes or anti-nodes at positions 2260 or 2250, we will not be able to measure motion at these locations if we measure displacement along these node lines. Note that this means that displacement-sensitive interferometric measurements are insensitive to motion at these points, while OBD measurements are sensitive to motion at these points. Furthermore, the derivative or slope measured by OBD will have a similar zero line, where OBD will essentially not measure the response, while the interferometer will measure a non-zero amplitude. This is well known in the art, see, for example. The location and excitation frequency of these zero lines or anti-node lines are controlled by the boundary conditions acting on the cantilever, including tip excitation, long-range electrostatic forces, cantilever damping, and other effects.

[0215] As discussed above, symmetry means that, at least at low frequencies, the displacement of the interferometric measurement has a zero region where the response to various components is negligible. For example, due to Therefore, the central longitudinal axis 2100 will not respond to lateral excitation. A similar argument applies to longitudinal excitation at the x-coordinate directly above the tip, where the oscillating motion has a node. 2200. The intersection of these two nodes occurs above the tip 1020, meaning that the displacement measured at this point contains only information about the vertical tip motion δz, because... and .

[0216] The x and y coordinates of the planar view point are experimentally observable and are typically measured using a camera or a position encoder on an AFM. Cantilever-related quantities, length L, and tip height h can also be measured directly and estimated according to the manufacturer's specifications or other characterization methods known in the art.

[0217] By shifting the tip by a known or approximately known amount, the partial derivatives of the cantilever shape at the location of the light spot can be estimated experimentally. This can be achieved through force curves and x- or y-modulation measurements. Furthermore, these can be estimated theoretically from analytical solutions such as Euler-Bernoulli solutions or finite element simulations of the actual cantilever geometry and materials, as well as other methods known in the art.

[0218] A powerful feature of this invention is that many methods already developed for lateral and longitudinal calibration of OBD-type AFMs can be used in this invention by replacing the OBD spot with an interference spot that is laterally and / or longitudinally offset. These methods include: (i) applying force directly to the cantilever beam at a known location, (ii) modulation using a suspension platform, (iii) the "wedge method"—scanning two inclined surfaces and measuring the friction ring, and (iv) measuring torsional resonance.

[0219] Once the quantity is determined , and Equation (1) still contains three unknowns, namely the strain components at the tip. , and One way to determine these quantities is through three independent displacements at different locations on the surface of the cantilever. As discussed above, and as we will explore below, this can be demonstrated through sequential and / or parallel interferometry.

[0220] Figure 30000 shows the top of the cantilever, where multiple spot locations for measuring displacement are located. In this example, the measurement locations are displacements along the principal Cartesian axis, but this is not required. (Tip) , and The motion causes displacement and tilting of the cantilever body. In the following analysis, we will assume that the cantilever behaves like a rigid body. Then, the relationship between the displacement measured on the top surface of the cantilever and the three-dimensional motion of the tip can be directly calculated. In this case, a useful concept is that the tip location, the position directly above the tip on the top surface of the cantilever, and the measurement point form a geometric triangle. As the tip moves, the other two points in this triangle must also move, thus the relationship between the measurement point and the tip motion can be calculated using simple trigonometric methods.

[0221] A rigid probe approximation may be insufficient in some cases. We can use more complete Euler-Bernoulli models, other analytical models, or computer simulations of structures, such as those that can be modeled using the finite element method. The results of these models can then be used to better approximate the cantilever curvature at the measurement location, for example, by including quadratic terms in the lateral coordinate system.

[0222] In the example below, if we assume the cantilever can be considered a rigid body near the tip, then the analysis of the response becomes a simple geometric problem. The IDS (Interferometer Detection Sensor) point is located on the back side of the cantilever, on either side of the tip axis, at position [missing information]. In this case, the amplitude measured by the IDS at both locations will be given by a complex expression.

[0223] 2. ,

[0224] 3. ,

[0225] and

[0226] 4. .

[0227] In expressions (2)-(4), we have separated the slowly changing “DC” motion from the rapidly changing modulated “AC” component. This is for the convenience of PFM measurements in this discussion, since the signal of interest in this case is the amplitude at the potential driving frequency. In fact, the vertical strain... In practice, this can be used to control the vertical load on a tip of a sample. This invention covers numerous examples that utilize multiple frequencies, including very high and very low (DC) observable responses. While we have isolated these for PFM, there are many other types of measurements, such as nanomechanical or nanorheological measurements, where slowly changing terms may contain very important viscoelastic information.

[0228] Symmetry means that the coupling between the lateral tip motion and the vertical displacement of the cantilever surface is essentially zero along the central axis of symmetry of the cantilever 6100. Similarly, when the cantilever is strongly coupled to the sample surface ( However, when swaying is permitted, there should be a similar zero axis 6110, where the longitudinal excitation is not coupled to the vertical surface motion. These locations can be used to select measurement points such that the measurements contain a specific mixture of tip displacement components.

[0229] From Figure 30000, we will use the coordinates of the spot position offset from the tip (w5) to estimate the in-plane sensitivity factor. We will also assume that the cantilever is parallel to the sample surface (θ = 0). We will use the notation... , , and To describe a geometric "lever arm" that couples in-plane tip motion to a vertical displacement measured by interferometry, such as... Figure 5 As shown, this will result in an experimentally observable displacement at the following interferometer measurement locations:

[0230] 5.

[0231] 6.

[0232] 7.

[0233] 8.

[0234] Equation (5-8) can be solved to obtain a complete three-dimensional expression for the tip trajectory, which is entirely represented by experimentally observable values:

[0235] 9.

[0236] 10.

[0237] 11.

[0238] and

[0239] 12.

[0240] By placing measurement points along the axis of symmetry of the cantilever, and recognizing that three independent measurements are sufficient to solve for the three unknowns, the analysis can be simplified by 31000.

[0241] 31000 shows three measurement positions, W1, W2, and W3. W1 is located directly above the cantilever tip, at which position W1 is sensitive only to the vertical deflection displacement of the cantilever tip. W2 and W3 are displacements along the Y-axis and X-axis, respectively. At these positions, they are sensitive to a mixture of the vertical motion and in-plane motion of the tip. For example, W2 would be a combination of the vertical motion and lateral displacement of the cantilever tip, while W3, displaced along the X-axis or longitudinal axis, would include a mixture of contributions from vertical and in-plane longitudinal tip motion.

[0242] This allows the gain factor to be simplified to and Meanwhile, other gain factors are essentially zero. Then, equation 9-12 can be simplified to estimate the three-dimensional tip motion:

[0243] 13.

[0244] 10.

[0245] and

[0246] 11. .

[0247] For completeness, Figure 33000 shows another possible case, this time where the measurement point is substantially away from the zero line, with the zero point located above the tip. In this case, all three measurements w1, w2, and w3 will contain a mixture of all three components of the tip motion.

[0248] Figure 5 Another embodiment is shown, where the measurements of two of the three coordinates are over-constrained. In this case, measurements are taken along the horizontal axis at three locations: 52000, 52100, and 52200. The measurements at the three spot locations 52000, 52100, and 52200 can be used to form the images shown. 52050 corresponds to location LF2000, image 52150 corresponds to location 52100, and image 52250 corresponds to measurement location 52200. The circled pixels in all three images are selected to be plotted using a straight-line fitting method. These three points can be fitted using a standard least-squares straight-line fitting procedure, and when plotted relative to the horizontal position, they will produce the Y-intercept and slope of the resulting straight line. In this case, if the straight line is centered at the tip, the Y-intercept of the fitted line is... The slope allows us to use the relational formula Calculate the plane of the tip Motion. This method can be extended to multiple measurements along the horizontal axis to increase the confidence of the fitted line. Clearly, it can also be extended to other axes, particularly the vertical axis of the cantilever. In this case, images of the vertical and in-plane motion of the tip are obtained.

[0249] Figure 6 A series of measurements based on the above discussion are shown, in which the complete three-dimensional motion of the tip is measured using a series of five measurement points circled in the figure. Components are used Figure 5 The technology described in the text is estimated, while The components are estimated using a similar method, but only using points measured along the x-axis. In both cases, also... An estimate was made and plotted on the right side of the figure. Note that in this specific case, the microscope used also has an OBD detector at the fixed OBD spot to operate the Z-feedback loop during the measurement. This is one approach; however, the interferometer signal can also be used for the Z-feedback loop. In this case, since the interferometer spot position is located at different points on the cantilever surface, care must be taken to adjust the setpoint to account for the different sensitivities at different spot positions.

[0250] In some cases, it is best to use a combination of the interferometer signal and the simultaneously measured OBD deflection signal to estimate the components of vertical and in-plane motion. Figure 7This embodiment is illustrated, in which the interferometer and the OBD spot (different in some embodiments, the same spot in others) are both placed directly above the tip. The interferometer is used to measure displacement in the vertical direction, while the OBD signal is used to measure the local slope at the same location. In this case, we use two independent interferometer measurements instead of one interferometer measurement and one OBD measurement. It should be clear that both methods are sufficient to define the shape of the cantilever tip and thus resolve the in-plane and vertical motion of the tip.

[0251] The shape of a cantilever can be better described by a higher-order function, such as a quadratic function. While a linear approximation can be determined by two-point measurements, higher-order functions may require more measurement points. More measurement points may have the advantage of better defining the uncertainties and errors in the measurement.

[0252] As is well known in the art, some cantilever 1000s have a "point view" feature, such as Figure 8 As shown, the tip extends beyond the end of the cantilever by a distance R, making it visible from above 1100. This can be advantageous for positioning the tip on the sample surface with high positional accuracy. In this case, another embodiment of the invention is required. It is difficult or even impossible to place the spot directly above the tip 1100 while still reflecting enough light back to the interferometer to measure the tip movement. In this case, the spot can be positioned at a distance from the tip, for example... At a known distance, the interferometer operation is fully optimized for vertical position measurement.

[0253] Figure 8 The undeflected cantilever 81100 is shown, with a tip view showing the tip 1100 protruding beyond the cantilever end R. In 81200, the magnitude of cantilever deformation is greatly exaggerated; typical tip 1100 motion is on the nanometer scale, while many cantilever scales are on the tens to hundreds of micrometer scale. In this embodiment, two interferometric measurement points are located at... and At this location, its position allows sufficient light to be reflected back to the interferometer detector. In the 81200, the cantilever deflects due to vertical and in-plane motion. This changes the shape of the cantilever, and consequently alters... and The measured value at the location, the change is and Two measurements and This allows the slope of the deflection cantilever body to be extrapolated to a distance R beyond the cantilever tip. This is a common technique for inferring the position of the cantilever tip (see, for example, Labuda et al.). In short, the vertical tip motion is determined by… Given. Similarly, the in-plane motion of the tip is given by Description. The estimate is within the rigid tip limit. It also assumes that the effects of other forces (such as electrostatic forces from the human body) are negligible.

[0254] If these assumptions do not hold, it may be necessary to invoke different models such as the Euler-Bernoulli beam model or numerical finite element simulation. In this case, this approach remains powerful because it can be used to fit more complex and potentially more accurate models of cutting-edge motion, rather than to a simple straight line, such as a measurement point, as in the example above. and And possibly more measurement points on the back of the cantilever. Note that, Figure 7 In this embodiment, slope measurement using OBD and displacement measurement using an interferometer are sufficient to infer tip motion. This method eliminates the need for two interferometric measurement points.

[0255] The inventors have noted that, for modulation measurements, it is advantageous to move the scanning tip relative to the surface scanning tip in a direction orthogonal to the in-plane component of the measurement. For example, if the microscope is configured to measure the y-component of the in-plane response, it is preferable to move from one measurement point to another by traveling primarily in the x-direction. This may be less important if the tip moves in a manner that keeps it substantially stationary during the measurement.

[0256] As discussed above, OBD measurements are affected by crosstalk between the longitudinal and lateral curvature of the cantilever. This may stem from misalignment between the cantilever coordinate system and the OBD detector coordinate system. Although possible, correcting this misalignment is difficult and may require repetition when a new cantilever is mounted into the AFM system. (See, for example, Crosstalk Correction in Atomic Force Microscopy, A. Hoffmann, T. Jungk, and E. Soergel, Review of Scientific Instruments, Vol. 78, No. 1, 2007).

[0257] Interferometric testing offers a simple solution to this problem. Since the interferometer is insensitive to displacement, the mixing of components can be controlled by selecting the position of the light spot at the top of the cantilever in the cantilever's reference frame. This... Figure 4 The diagram illustrates a cantilever that happens to be loaded at an angle. The position of the light spot is determined by positioning it within the reference frame of the cantilever, specifically relative to the tip position and the longitudinal and transverse axes of the cantilever. This ensures that the measurement is performed within the same reference frame of the lever and substantially avoids crosstalk between the longitudinal, transverse, and / or vertical directions.

[0258] It should be understood that while the methods described above can be performed continuously by as few as a single interferometric sensor, these measurements can be improved by performing them with multiple interferometric sensors deployed at multiple locations on the cantilever.

[0259] Positioning the light spot away from the tip can optimize the sensitivity of the IDS to one or more specific eigenmodes of the cantilever's dynamic response. This can be optionally achieved while intentionally avoiding sensitivity to another eigenmode, for example, by positioning the light spot at the null position of the mode to be avoided on the cantilever. In this approach, the normal or torsional eigenmode is first identified, which can be achieved by performing thermal tuning and identifying the frequency of the Gaussian distribution in the resulting power spectral density. Alternatively, drive tuning can be performed using photothermal actuation, piezoelectric actuators, or any other actuator known to those skilled in the art, and the result of this tuning can be used to identify the eigenmode, and optionally, the spatial location of the eigenmode null position. The frequency range of eigenmodes for a particular cantilever can optionally be pre-listed and used to aid in searching for resonant frequencies or to identify which frequency corresponds to which normal or torsional eigenmode. Once the frequencies of the eigenmodes are established, the light spot is moved until the measured amplitude of a particular eigenmode is maximized, or a quantity that is a function of the amplitudes of multiple eigenmodes is maximized, or until the amplitude of a particular eigenmode is reduced to noise only. Root-finding or other optimization methods can be used to determine which direction the light spot should move to maximize or minimize the response to one or more eigenmodes. Alternatively, the light spot can be moved in preset increments until the response of interest reaches its maximum or minimum value.

[0260] In some cases, it may be desirable to have a prescribed mixture of modes in the measured signal. In such cases, the spot position can be adjusted to optimize the overall experimental objective. For example, in the case of bimodal and correlation techniques, two or more resonant modes are used to measure sample shape and properties. Typically, it is desirable for one mode to operate at a relatively large amplitude, while the others operate at relatively small amplitudes. In this case, it may be advantageous to position the spot such that the sensitivity to small amplitude measurements is maximized, even if the sensitivity to large amplitude modes may be reduced as a result. In another case, it may be useful to perform force curve analysis while measuring the characteristics of one or more resonants of a cantilever. In this case, it may be advantageous to place the spot in a position that maximizes sensitivity to the minimum signal, at the expense of some sensitivity to larger signals.

Claims

1. A method for operating a scanning probe microscope, the scanning probe microscope comprising: A probe having a cantilever with a tip; A sample and a sample holder, the sample holder being arranged to hold the sample for measurement using the tip of the cantilever; A light source is arranged to emit one or more beams of light onto the surface of the cantilever, each beam of light forming a measurement point on the surface of the cantilever; An optical component configured to adjust the position of each measuring point on the surface of the cantilever; as well as A photodetector assembly for measuring light reflected from the surface of the cantilever to measure the motion of the cantilever based on the light reflected from each measurement point; The method includes the following steps: (a) Position the first measuring point at a first location on the surface of the cantilever; (b) While the tip interacts with the sample, the cantilever displacement at the first position is measured; (c) While the tip interacts with the sample, the cantilever deflection at the first position is measured; and (d) Calculate one or more components of the cantilever motion based on the cantilever displacement measured in step (b) and the cantilever deflection measured in step (c).

2. The method according to claim 1, wherein, The scanning probe microscope also includes an actuator assembly configured to adjust the distance between the tip and the sample along the optical axis of the light source.

3. The method according to claim 1 or 2, wherein, The cantilever includes a zero point located on the surface of the cantilever, wherein the zero point is a position on the cantilever where the movement of the cantilever is only affected by a vertical force, and wherein the first position is the zero point.

4. A scanning probe microscope, comprising: A probe, the probe having a cantilever with a tip; A sample holder, the sample holder being arranged to hold a sample for measurement using the tip of the cantilever; A light source is arranged to emit one or more beams of light onto the surface of the cantilever, each beam of light forming a measurement point on the surface of the cantilever; An optical component configured to adjust the position of each measuring point on the surface of the cantilever; as well as A photodetector assembly for measuring light reflected from the surface of the cantilever to measure the motion of the cantilever based on the light reflected from each measurement point; The scanning probe microscope is configured to perform the method according to any one of claims 1 to 3.

5. The scanning probe microscope of claim 4, further comprising an actuator assembly configured to adjust the spacing between the tip and the sample along the optical axis of the light source, the sample being held by the sample holder.

6. A method for operating a scanning probe microscope, the scanning probe microscope comprising: A probe having a cantilever with a tip, wherein the cantilever includes a zero point on the surface of the cantilever, wherein the zero point is a position on the cantilever where the movement of the cantilever is only affected by a vertical force; A sample and a sample holder, the sample holder being arranged to hold the sample for measurement using the tip of the cantilever; A light source is arranged to emit one or more beams of light onto the surface of the cantilever, each beam of light forming a measurement point on the surface of the cantilever; An optical assembly configured to adjust the position of each measuring point on the surface of the cantilever; and A photodetector assembly for measuring light reflected from the surface of the cantilever to measure the motion of the cantilever based on the light reflected from each measurement point; The method includes the following steps: (i) Position the first measuring point at a first position off the zero point on the surface of the cantilever; (ii) While the tip interacts with the sample, the cantilever motion at the first position is measured; (iii) Position the second measuring point on the surface of the cantilever at a second position offset from the zero point and the first position; (iv) While the tip interacts with the sample, the cantilever motion at the second position is measured; and (v) Calculate one or more components of the cantilever motion based on the relative position of each of the first and second positions with respect to the zero point and the measurements taken from the first and second positions in steps (ii) and (iv).

7. The method according to claim 6, wherein, The scanning probe microscope also includes an actuator assembly configured to adjust the distance between the tip and the sample along the optical axis of the light source.

8. The method according to claim 6 or 7, wherein each of the one or more components calculated in step (v) is parallel to or perpendicular to the optical axis of the light source.

9. The method of claim 8, wherein at least one of the one or more components calculated in step (v) is perpendicular to the optical axis of the light source and aligned with the major axis or the minor axis of the cantilever, wherein, The short axis is perpendicular to the long axis along the surface of the cantilever.

10. The method according to any one of claims 6 to 9, wherein step (v) comprises: Based on the relative position of each of the first and second positions with respect to the zero point and the measurements taken from the first and second positions in steps (ii) and (iv), a first component of the cantilever motion is calculated; as well as Based on the relative position of each of the first and second positions with respect to the zero point and the measurements taken from the first and second positions in steps (ii) and (iv), the second component of the cantilever motion is calculated; The second component is perpendicular to the first component.

11. The method according to any one of claims 6 to 10, wherein, The first position and the second position are symmetrical about the zero point.

12. The method according to any one of claims 6 to 11, wherein, A straight line drawn between the first position and the second position is substantially parallel to the major axis of the cantilever, or wherein a straight line drawn between the first position and the second position is substantially parallel to the minor axis of the cantilever, wherein the minor axis is perpendicular to the major axis along the surface of the cantilever.

13. The method according to claim 12, wherein, The first position and the second position are respectively located on the long axis of the cantilever, or the first position and the second position are respectively located on the short axis of the cantilever.

14. The method according to any one of claims 6 to 13, wherein, The cantilever motion is the cantilever displacement, or one of them. The cantilever motion is cantilever deflection.

15. The method according to claim 14, wherein, When the cantilever motion is cantilever displacement, the cantilever motion is measured using an interferometric displacement sensor, and when the cantilever motion is cantilever deflection, the cantilever motion is measured using a beam deflection method.

16. The method according to claim 15, wherein, The interferometric displacement sensor includes a differential interferometer.

17. The method according to any one of claims 14 to 16, wherein step (ii) comprises: (a) While the tip interacts with the sample, the cantilever displacement at the first position is measured; (b) while the tip interacts with the sample, the cantilever deflection at the first position is measured; And / or step (iv) includes: (a) measuring the cantilever displacement at the second position while the tip interacts with the sample; (b) while the tip interacts with the sample, the cantilever deflection at the second position is measured.

18. The method according to any one of claims 6 to 17, wherein, The steps are performed sequentially.

19. The method according to any one of claims 6 to 17, wherein, Steps (ii) and (iv) are performed simultaneously.

20. The method according to any one of claims 6 to 19, wherein, Step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first and second positions with respect to the zero point, the height of the tip, and measurements taken from the first and second positions in steps (ii) and (iv).

21. The method according to any one of claims 6 to 20, further comprising the step of: (vi) Position the third measuring point on the surface of the cantilever at a third position, offset from the zero point and from the first and second positions; as well as (vii) While the tip interacts with the sample, the cantilever motion at the third position is measured; as well as Step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first position, the second position, and the third position relative to the zero point and the measurements taken from steps (ii), (iv), and (vii) at the first position, the second position, and the third position.

22. The method according to claim 21, further comprising the step of: (viii) Position the fourth measuring point on the surface of the cantilever at a fourth position, offset from the zero point and the first, second, and third positions; as well as (ix) While the tip interacts with the sample, the cantilever motion at the fourth position is measured; as well as Step (v) includes calculating one or more components of the cantilever motion based on the relative position of each of the first position, the second position, the third position, and the fourth position relative to the zero point and the measurements taken from steps (ii), (iv), (vii), and (ix) at the first position, the second position, the third position, and the fourth position.

23. The method according to claim 21 or 22, wherein, The one or more components of the cantilever motion in step (v) include a first component, a second component, and a third component, wherein the first component, the second component, and the third component are each perpendicular to each other.

24. The method according to claim 22 or claim 23 when relying on claim 22, wherein, The third and fourth positions are symmetrical about the zero point.

25. The method according to any one of claims 22 to 24, wherein, The third position and the fourth position are each located on the major axis of the cantilever, or the third position and the fourth position are each located on the minor axis of the cantilever, wherein the minor axis is perpendicular to the major axis along the surface of the cantilever.

26. The method according to any one of claims 6 to 25, wherein, The zero point is substantially aligned with the tip along the optical axis of the light source.

27. The method according to any one of claims 6 to 26, wherein, The zero point is identified based on at least one of the following: user input, calibration procedure, value stored in memory, or image recognition of the surface of the cantilever.

28. The method according to any one of claims 6 to 27, wherein, The method includes executing a computer program to cause the scanning probe microscope to perform each step of the method.

29. A scanning probe microscope, comprising: A probe having a cantilever with a tip, wherein the cantilever includes a zero point on the surface of the cantilever, wherein the zero point is a position on the cantilever where the movement of the cantilever is only affected by a vertical force; A sample holder, the sample holder being arranged to hold the sample for measurement using the tip of the cantilever; A light source is arranged to emit one or more beams of light onto the surface of the cantilever, each beam of light forming a measurement point on the surface of the cantilever; An optical assembly configured to adjust the position of each measuring point on the surface of the cantilever; and A photodetector assembly for measuring light reflected from the surface of the cantilever to measure the motion of the cantilever based on the light reflected from each measurement point; The scanning probe microscope is configured to perform the method according to any one of claims 6 to 28.

30. The scanning probe microscope of claim 29, further comprising an actuator assembly configured to adjust the spacing between the tip and the sample along the optical axis of the light source, the sample being held by the sample holder.

31. The scanning probe microscope of claim 29 or 30, further comprising a differential interferometer configured to position a first measurement point and a second measurement point on the surface of the cantilever at a first position and a second position respectively off-zero.

32. A probe for performing the method of any one of claims 6 to 28, the probe having a cantilever with a tip; in, The cantilever includes an unsupported first end and a second end supported by the probe, wherein the tip is disposed at the first end; and The first region of the cantilever has a wider width than the second region of the cantilever, wherein the first region is closer to the first end, and the second region is closer to the second end.

33. The probe according to claim 32, wherein, The width of the first end is greater than the width of the second end.

34. The probe according to claim 32 or 33, wherein, The cantilever includes a surface for receiving measurement points, the surface having a major axis and a minor axis.

35. The probe according to any one of claims 32 to 34, wherein, The first region has a substantially uniform width, and / or the second region has a substantially uniform width.

Images